Under what conditions is the matrix `A^2-B^2=(A-B)(A+B)` is true?

Under what conditions is the matrix equation A^2-B^2=(A-B)(A+B) is true?

Under what conditions is the matrix equation A^(2)-B^(2)=(A-B)(A+B) is true?

(a) Under what conditions energy is conserved ? (b) What is the only restriction to the principle of conservation of energy ?

Under what condition will the equality : vec A xx vec B = vec A . vec B hold good ?

Restate the following statements with appropriate conditions, so that they become true. (i) If a^2 gt b^2 , then a gt b .

Under what condition |vec(A)+vec(B)| = |vec(A)|+|vec(B)| holds good?

Under what condition |vec(A)+vec(B)| = |vec(A)|+|vec(B)| holds good?

a_1x+b_1y+c_1=0, a_2x+b_2y+c_2=0 Under what condition the above equations represent a unique solution.

a_1x+b_1y+c_1=0, a_2x+b_2y+c_2=0 Under what condition the above equations represent infinitely many solution.

If vec(A) + vec(B) = vec(C ) under what condition A^(2)+B^(2) will be equal to C^(2) ?